The foundation of Physics (Newton's Second Law of Motion); 50 minutes + 30 minutes extension.
State Standards:
PS3 (9-11)–9 Students demonstrate an understanding of forces and motion by…
9b using Newton’s Laws of Motion and the Law of Conservation of Momentum to predict the effect on the motion of objects.
National Standards:
CONTENT STANDARD B: As a result of their activities in grades 9-12, all students should
develop an understanding of...
Motions and forces
Context of Lesson:
This lesson is designed to be a continuation of the topic of Newton's laws of motion. Newton's second law of motion is one of greatest mathematical significance. This law of F=ma is used to derive nearly every kinematic equation and law of planetary motion that exists. Though none of those derivations can be computed without a firm grasp of all the calculeses; it is beneficial that students can be able to understand that F=ma is a universal equation that works in any macroscopic situation involving any number of objects and forces. Some of the key focuses of this lesson include the following:
Defining Newton's Second Law
Understanding the units of a Newton
Defining weight
Understanding that weigh is a force caused by gravity
Solving problems involving force, mass, and acceleration
Finding the mass of an object if the weight is given
Understanding that US pounds is a measure of weight not mass
Exploring the idea of tension in massless strings
Opportunities to Learn:
Students will experience much discussion that is mathematically driven in this lesson. The students will gain a better understanding of how to communicate in terms of mathematics and algebra. Interpersonal communication and logical mathematical are the primary MI's stressed in this lesson.
Depth of Knowledge:
-As discussed in the objectives and main lesson plan, the depth of knowledge in this lesson is focussed in the following categories:
Remembering
Understanding
Applying
Analyzing
Prerequisite Knowledge:
-An understanding of forces and Newton's first law of motion
Plans for Differentiating Instruction:
-For students who may not be visual/spatial MI's, I will present the students with verbal explanations to all the sections of this lesson and not simply read off the PowerPoint presentation. Students who are visual/spatial can simply take notes.
Accommodations and modifications:
Environmental factors:
Materials:
Books
Mini-whiteboards
Smartboard
Homework Ditto
Objectives:
Some of the key focuses of this lesson include the following:
Define Newton's Second Law
Understand the units of a Newton
Define weight
Understand that weight is a force caused by gravity
Solve problems involving force, mass, and acceleration
Find the mass of an object if the weight is given
Understand that US pounds is a measure of weight not mass
Explore the idea of tension in massless strings
Instruction:
Opening:
First 5 minute of class:
Settling in and class attendance
5:00-20:00 into class:
Recap on everything we learned from the previous 2 lessons involving forces and inertia.
Recap on the inquiry assignment from the previous lesson.
Ask the students what direction the blocks moved when hit by the ball-bearings.
Reach an agreement with all the students that if some forces is exerted on an object it moves in the direction of that force. Therefore we can generalize that "a α F(net)", where α (alpha) means proportional. Explain that α is like an "=" sign. Just it does not necessarily mean "equal".
Next, discuss how the heavier an object was the less it would move. Therefore the less it accelerated. Therefore we can say that "a α 1/m", where "m" is the mass. Meaning that acceleration is inversely proportional to mass.
Therefore, if we combine these two reasonings we find that "a α F(net)/m"
Engagement:
20:00-35:00 into class:
Have the students open their books to page 103 and view the following diagram:
Take whatever course necessary to explain the above diagram. From this diagram we can arrive at Newton's 2nd law of motion "F=ma". From here students may question why we switched the α to an "=" sign. Now might be a respectable time to go into a discussion of the differences between a theory and a law.
It is important that students leave high school with a grasp of the differences between hypotheses, theories, and laws. Newton's 2nd law provides us with enough ground both qualitatively and quantitatively to attack this head on.
Hypothesis: students should understand that a hypothesis is any idea that has a subsequent procedure for further experimentation. Most often this idea has some theoretical calculations as backing.
Theory: A theory is any hypothesis that has "stood the test of time". For example, Pythagorean theorem is a theory that is used nearly every aspect of mathematics and science. It is something that has been tested time and time again.
Scientific Law: The biggest misconception students have is that hypotheses when test enough graduate to theories, and theories that work many many times become laws. In fact this is not true. Laws are Scientific phenomena that occur in nature as observables. No one is quite sure how or why they work. But they are true. For instance, Newton's 2nd law of motion is that F=ma. There is no way to derive F=ma, it just simply works as seen in our previous thought process. For more readings on confusions between theories and laws: Thanks for including the link below so I understand your concerns. My personal view is that once you sift through the misnomers, laws are actually axioms, or assumptions. Newton's Laws are just names, like Schrodinger's equation. The question for you is how to illustrate the points you think are important. Here is a brilliant example of this.
Discuss the SI unit of force "Newton" (N). Verify that a newton is a kg(m/s^2) through, F=ma.
Define weight as the force exerted on a person/object from the Earth. In which case F=w, a=g, and g=9.81(m/s^2). Make sure to clear up the misconception of weight being how much mass something or someone has. It is also notable to mention that we as US citizens lie everyday when we give our "weight" in pounds. In fact, pounds are a measure of mass and therefore to accurately give our weight we must multiply our pounds by 10! And you think your subconscious now! Huh? I don't understand this. There are pounds-force (Which is what we see when we stand on scales) and pounds-mass, which I have never seen used. I have used physics books that use "slugs" to measure mass.
What about the down-to-earth idea that a Newton weighs about a 1/4 pound, and is the weight of 100 grams. Shouldn't students be able to lift 100 grams and think about newtons?
Personally, I would cover F=ma and then types of forces over several days. How many chapters does this span in your text?
Closure:
45:00-50:00 into class:
Wrap up the class by having the students compute their weight in newtons starting with F=ma. DO NOT let them skip right to w=mg because they will never see the connection between F=ma and what substitutions make it w=mg! THIS IS KEY!
Extension:
50:00-65:00 into class:
Have the students work in groups of no more than 3 and work on problems in the book to calculate the weight of different objects.
65:00-80:00 into class:
Do example 4.1 on page 105 in the book about the tractor pulling the cart. Use class-fueled discussion to work through the problem. The problem starts by asking for the acceleration of the cart to the the force exerted on it by the tractor (mass given). From there it asks to apply a given frictional force that opposes the motion of the cart (feel free to substitute the force of the wind for friction so not to confuse them in future lessons). Afterward, it asks to recall equations from the kinematics chapter and find out how far the tractor has moved in 4 seconds. A very good exercise to help "tie it all together". Emphasize that all of physics is connected in some way! If there is time left over let them begin working on the ditto for homework with multiple problems using F=ma.
I am not quite understanding the "+30 minute extension." Can you teach during this time?
After collecting this ditto from the students, correcting it (WITH COMMENTS!), and handing it back to them; it would be best to perhaps quiz them on the material that following day (notify them first so they can review that homework). F=ma is one of the most important things a young scientist can grasp; therefore the extra time spent on this will only benefit them.
Rhode Island Department of Education Lesson Plan
Lesson Title:
The foundation of Physics (Newton's Second Law of Motion); 50 minutes + 30 minutes extension.State Standards:
PS3 (9-11)–9 Students demonstrate an understanding of forces and motion by…National Standards:
CONTENT STANDARD B: As a result of their activities in grades 9-12, all students shoulddevelop an understanding of...
Context of Lesson:
This lesson is designed to be a continuation of the topic of Newton's laws of motion. Newton's second law of motion is one of greatest mathematical significance. This law of F=ma is used to derive nearly every kinematic equation and law of planetary motion that exists. Though none of those derivations can be computed without a firm grasp of all the calculeses; it is beneficial that students can be able to understand that F=ma is a universal equation that works in any macroscopic situation involving any number of objects and forces. Some of the key focuses of this lesson include the following:Opportunities to Learn:
Students will experience much discussion that is mathematically driven in this lesson. The students will gain a better understanding of how to communicate in terms of mathematics and algebra. Interpersonal communication and logical mathematical are the primary MI's stressed in this lesson.Depth of Knowledge:
-As discussed in the objectives and main lesson plan, the depth of knowledge in this lesson is focussed in the following categories:Prerequisite Knowledge:
-An understanding of forces and Newton's first law of motionPlans for Differentiating Instruction:
-For students who may not be visual/spatial MI's, I will present the students with verbal explanations to all the sections of this lesson and not simply read off the PowerPoint presentation. Students who are visual/spatial can simply take notes.Accommodations and modifications:
Environmental factors:
Materials:
Objectives:
Some of the key focuses of this lesson include the following:Instruction:
Opening:
- First 5 minute of class:
Settling in and class attendance- 5:00-20:00 into class:
Recap on everything we learned from the previous 2 lessons involving forces and inertia.Recap on the inquiry assignment from the previous lesson.
Ask the students what direction the blocks moved when hit by the ball-bearings.
Reach an agreement with all the students that if some forces is exerted on an object it moves in the direction of that force. Therefore we can generalize that "a α F(net)", where α (alpha) means proportional. Explain that α is like an "=" sign. Just it does not necessarily mean "equal".
Next, discuss how the heavier an object was the less it would move. Therefore the less it accelerated. Therefore we can say that "a α 1/m", where "m" is the mass. Meaning that acceleration is inversely proportional to mass.
Therefore, if we combine these two reasonings we find that "a α F(net)/m"
Engagement:
- 20:00-35:00 into class:
Have the students open their books to page 103 and view the following diagram:Take whatever course necessary to explain the above diagram. From this diagram we can arrive at Newton's 2nd law of motion "F=ma". From here students may question why we switched the α to an "=" sign. Now might be a respectable time to go into a discussion of the differences between a theory and a law.
It is important that students leave high school with a grasp of the differences between hypotheses, theories, and laws. Newton's 2nd law provides us with enough ground both qualitatively and quantitatively to attack this head on.
Hypothesis: students should understand that a hypothesis is any idea that has a subsequent procedure for further experimentation. Most often this idea has some theoretical calculations as backing.
Theory: A theory is any hypothesis that has "stood the test of time". For example, Pythagorean theorem is a theory that is used nearly every aspect of mathematics and science. It is something that has been tested time and time again.
Scientific Law: The biggest misconception students have is that hypotheses when test enough graduate to theories, and theories that work many many times become laws. In fact this is not true. Laws are Scientific phenomena that occur in nature as observables. No one is quite sure how or why they work. But they are true. For instance, Newton's 2nd law of motion is that F=ma. There is no way to derive F=ma, it just simply works as seen in our previous thought process. For more readings on confusions between theories and laws: Thanks for including the link below so I understand your concerns. My personal view is that once you sift through the misnomers, laws are actually axioms, or assumptions. Newton's Laws are just names, like Schrodinger's equation. The question for you is how to illustrate the points you think are important. Here is a brilliant example of this.
- 35:00-45:00 into class:
Discuss the SI unit of force "Newton" (N). Verify that a newton is a kg(m/s^2) through, F=ma.Define weight as the force exerted on a person/object from the Earth. In which case F=w, a=g, and g=9.81(m/s^2). Make sure to clear up the misconception of weight being how much mass something or someone has. It is also notable to mention that we as US citizens lie everyday when we give our "weight" in pounds. In fact, pounds are a measure of mass and therefore to accurately give our weight we must multiply our pounds by 10! And you think your subconscious now! Huh? I don't understand this. There are pounds-force (Which is what we see when we stand on scales) and pounds-mass, which I have never seen used. I have used physics books that use "slugs" to measure mass.
What about the down-to-earth idea that a Newton weighs about a 1/4 pound, and is the weight of 100 grams. Shouldn't students be able to lift 100 grams and think about newtons?
Personally, I would cover F=ma and then types of forces over several days. How many chapters does this span in your text?
Closure:
- 45:00-50:00 into class:
Wrap up the class by having the students compute their weight in newtons starting with F=ma. DO NOT let them skip right to w=mg because they will never see the connection between F=ma and what substitutions make it w=mg! THIS IS KEY!Extension:
- 50:00-65:00 into class:
Have the students work in groups of no more than 3 and work on problems in the book to calculate the weight of different objects.- 65:00-80:00 into class:
Do example 4.1 on page 105 in the book about the tractor pulling the cart. Use class-fueled discussion to work through the problem. The problem starts by asking for the acceleration of the cart to the the force exerted on it by the tractor (mass given). From there it asks to apply a given frictional force that opposes the motion of the cart (feel free to substitute the force of the wind for friction so not to confuse them in future lessons). Afterward, it asks to recall equations from the kinematics chapter and find out how far the tractor has moved in 4 seconds. A very good exercise to help "tie it all together". Emphasize that all of physics is connected in some way! If there is time left over let them begin working on the ditto for homework with multiple problems using F=ma.I am not quite understanding the "+30 minute extension." Can you teach during this time?
Assessment:
- Homework Ditto as formative assessment.
After collecting this ditto from the students, correcting it (WITH COMMENTS!), and handing it back to them; it would be best to perhaps quiz them on the material that following day (notify them first so they can review that homework). F=ma is one of the most important things a young scientist can grasp; therefore the extra time spent on this will only benefit them.Reflections
(only done after lesson is enacted)Student Work Sample 1 – Approaching Proficiency:
Student Work Sample 2 – Proficient:
Student Work Sample 3 – Exceeds Proficiency: